Least Common Multiple (LCM) of 119 and 13
The least common multiple (LCM) of 119 and 13 is 1547.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 119 and 13?
First, calculate the GCD of 119 and 13 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 13 = 9 remainder 2 |
| 2 | 13 ÷ 2 = 6 remainder 1 |
| 3 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 126 | 1260 |
| 130 and 41 | 5330 |
| 168 and 38 | 3192 |
| 23 and 85 | 1955 |
| 54 and 160 | 4320 |